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In this paper, a weighted least-squares method is presented to design one-dimensional and two-dimensional variable fractional delay allpass filters. First, each coefficient of the variable allpass filter is expressed as the polynomial of the fractional delay parameter. Then, the nonlinear phase error is approximated by a weighted equation error such that the cost function can be converted into a quadratic form. Next, by minimizing the weighted equation error, the optimal polynomial coefficients can be obtained iteratively by solving a set of linear simultaneous equations at each iteration. Finally, the design examples are demonstrated to illustrate the effectiveness of the proposed approach.